This is a 7900GS and it dose indeed require a 6 pin but that does not guarantee that the PSU in the XPS has a 6 pin but dose show that it can handle a graphics card using a Molex to 6 pin converter at the very least.
The 7900GS reccomends a 350 watt PSU and 22 amps on the 12 volt rail.
Edit. Forgot to look up the 9600GT. It requires "Minimum 400W or greater system power supply (with 12V current rating of 26A)"
also found some on newegg that required 450 watts so eather way it looks like you will need to upgrade your PSU.
No need to upgrade the psu for any video card that only require's a single power connector.
PS: Don't know where you are located but BestBuy has the PNY 9800 GT on sale for $105 and the 9800 GTX+ for $115, either of these would be a big improvement over a 9600GT, and will work with the stock psu.